循环群与循环群直积的同构表示

本文运用基础代数中有关循环群、直积、同构等理论，证明了一个循环群可以用另一组循环群的直积形式来同构表示。     

The interplay of representations and patterns of classroom discourse in science teaching sequences

The purpose of this study is to examines the relationship between the communicative approach of classroom talk and the modes of representations used by science teachers. Based on video data from two physics classrooms in Singapore, a recurring pattern in the relationship was observed as the teaching sequence of a lesson unfolded. It was found that as the mode of representation shifted from enactive (action based) to iconic (image based) to symbolic (language based), there was a concurrent and coordinated shift in the classroom communicative approach from interactive–dialogic to interactive–authoritative to non-interactive–authoritative. Specifically, the shift from enactive to iconic to symbolic representations occurred mainly within the interactive–dialogic approach while the shift towards the interactive–authoritative and non-interactive–authoritative approaches occurred when symbolic modes of representation were used. This concurrent and coordinated shift has implications on how we conceive the use of representations in conjunction with the co-occurring classroom discourse, both theoretically and pedagogically.     

关于解线性方程组的迭代法

给出了几个上三角迭代公式，讨论了它们的收敛性，给出了选代法的一个新的一般形式和一个矩阵迭代公式，一般形式为构造快速收敛的迭代提供了方便，矩阵迭代则是一种具有较快敛速的算法．讨论了迭代法进行消元的问题，误差估计的结果表明用迭代法进行消元是稳定的、可行的．     

Infants' cross-modal transfer from solid objects to their graphic representations

12-month-old infants were familiarized either tactually or visually with objects and then tested for visual recognition memory using either (1) the familiar and a novel object, (2) colored pictures of the objects, or (3) outline drawings of them. In Study 1, infants showed recognition memory on all 3 visual intramodal problems but showed cross-modal transfer only when objects were used as test stimuli. With increased familiarization times in Study 2, transfer from tactually presented samples to both pictorial displays was achieved, indicating that after feeling an object the infants were able to recognize it visually solely on the basis of its contour. With reduced familiarization times in Study 3, there was no evidence for transfer from visually presented samples to the 2 pictorial displays, replicating the pattern of results observed cross-modally in Study 1 and suggesting that, at least in certain respects, cross-modal and intramodal perception follow similar principles.     

Parents' representations of their children's mathematics learning in multiethnic primary schools

There is a growing concern that governmental calls for parental involvement in children's school mathematics learning have not been underpinned by research. In this article the authors aim to offer a contribution to this debate. Links between children's home and school mathematical practices have been researched in sociocultural studies, but the origins of differences within the same cultural group are not well understood. The authors have explored the notion that parents' representations of school mathematics and associated practices at home may play a part in the development of these differences. This article reports an analysis of interviews with parents of 24 children of Pakistani and White origin enrolled in primary schools in England, including high and low achievers in school mathematics. The extent to which the parents represented their own school mathematics and their child's school mathematics as the ‘same’ or ‘different’ are examined. In addition, ways in which these representations influenced how they tried to support their children's learning of school mathematics are examined. The article concludes with reflections on the implications of the study for education policy.     

对角优势矩阵及其迭代性质

本文主要讨论了对角优势矩阵的性质及其应用,并将二者作了简单的糅合。由于对角优势矩阵的非奇异性,正稳定性,且由其组成的系数方程用Jacobi和Gauss—Seidel迭代法均收敛的良性,使得对角优势矩阵在方程及矩阵中有其重要地位．     

由—迭代方程组引出的一些结论

对美国数学邀请赛9—7题的讨论已有报道．本拟给出另一种解释．原题为：     

“三个代表”是对历史唯物主义的丰富和发展

在世纪之交，江泽民同志提出了“三个代表”的思想。这一思想对于我们的改革和现代化建设具有深远的指导意义。本文就中国共产党为什么要提出和实施“三个代表”这一思想，以历史唯物主义的观点进行了分析论述。     

非扩张映射不动点带误差的迭代过程

在一致凸Banach空间中对非扩张映射讨论了带误差的Mann迭代过程的一些特性,将Reich的相应定理扩展到带误差Mann的迭代过程。     

Newton迭代法的应用研究

重点讨论了求解非线性方程根的Newton迭代法,根据方程的根的重数来确定：当为单根时,使用Newton迭代法;当为重根时,使用改进法;当根的重数不确定时,使用综合法。     

由一迭代方程组引出的一些结论

对美国数学邀请赛9-7题的讨论已有报道[1].本文拟给出另一种解释.原题为:求A2,这里A是方程x=19 9119 9119 9119 9119 91x①所有根的绝对值之和.首先,方程①右边易化为Ax BCx D(C≠0)的形式,于是,方程①可化为一元二次方程x(Cx D)=Ax B.②显然,方程②在复数域C内恰有两个解.其次     

一维抛物方程初边值问题拟多重网格预处理迭代法

把多重网格法和预处理方法结合起来用于一维抛物方程初边值问题上,得出用于一维抛物方程的预处理迭代矩阵。通过数值实验,证明此方法可行,并得出了收敛速度快,并且收敛性不依赖于w等结论。     

并行块SAOR迭代算法及其收敛性

推广了解线性方程组的SAOR迭代算法，给出了并行块SAOR迭代算法（简记为MBSAOR迭代法)模型，并在系数矩阵为块H—矩阵的条件下，证明了MBSAOR迭代算法的收敛定理。     

Schematic representations in arithmetical problem solving: Analysis of their impact on grade 4 students

While the value of ‘schematic representations’ in problem solving requires no further demonstration, the way in which students should be taught how to construct these representations invariably gives rise to various debates. This study, conducted on 146 grade 4 students in Luxembourg, analyzes the effect of two types of ‘schematic representation’ (diagrams vs. schematic drawings) on the solving of arithmetical problems. The results show that the presence of schematic representations has a clear positive effect on overall student performance and that a non negligible proportion of students manage to reuse the representations encountered in order to solve new problems. While showing an effect slightly in favor of diagrams as opposed to schematic drawings, our results do not really permit us to draw any conclusions about the form that these representations should take, in particular since a differential effect was observed depending on the type of problem.     

Preferred representations and knowledge acquisition

European Journal of Psychology of Education - There are two kinds of preferential representations. They are connected on the one hand to the degree of typicality of the instance in relation to the...     

线性方程组的距离迭代解法

目前,线性方程组的数值求解,常用的方法是Gauss-Seidel迭代法.Gauss-Seidel的收敛性要求条件很强.对于一般n元方程组,如果系数矩阵的秩小于n,则Gauss-Seidel迭代一般不能使用.本文所要介绍的距离迭代法,及其改进方法,折线迭代法,对于方程组基本上没有什么要求,只要有解,就一定能够得到.距离迭代法具有鲜明的几何意义,理论、方法十分朴素易懂,速度快,精度高,是一个值得推荐的优秀数值方法.     

Children's insecure representations of the interparental relationship and their school adjustment: the mediating role of attention difficulties

This study examined the role of attention difficulties as a mediator of associations between children's insecure representations of the interparental relationship and their school adjustment in a sample of two hundred and sixteen 6-year-old children. Consistent with hypotheses, findings from structural equation models indicated that observer ratings of children's insecure representations of interparental relationships in a story completion task predicted computerized task assessments and parent reports of children's attention difficulties 1 year later. Children's attention difficulties, in turn, were associated with concurrent levels of school problems and increases in school problems over a 1-year period as indexed by teacher reports. Attention difficulties accounted for an average of 34% of the association between insecure internal representations and school problems.     

线性递归序列与射影函数的迭代

给出了2阶实线性递归序列与1维实射影函数的迭代的关系,进而利用矩阵的幂得到2阶实线性递归序列的通项及极限性质。     

两类折线函数的迭代

作为非线性运算,迭代通常放大非线性函数的非线性性.单折点的折线函数是最简单的非线性函数.由于函数值在迭代下可以交叉于不同的子区间,折线的变化是复杂的.针对迭代指数趋于正无穷时折点个数问题,运用折线函数在子区间上的单调性分别给出折点个数保持不变、是一个正整数以及正无穷的充分条件.